Pie Chart Angle Calculator

Turn a category's value into the exact angle of its pie chart slice using angle = (value / total) x 360 degrees.

Quick Facts

Formula
Angle = (value / total) x 360 degrees
All slice angles in a chart always sum to 360 degrees.

Your Results

Calculated
Slice angle
-
Degrees of the full circle
Percentage of whole
-
Share of the total
Slice angle (radians)
-
Same angle in radians

Ready

Enter a category value and the total, then calculate.

How to calculate a pie chart angle

A pie chart divides a full circle among categories in proportion to their values. A full circle is 360 degrees, so each category's slice angle is simply its share of the total multiplied by 360:

Slice angle (degrees) = (category value / total of all values) × 360

Every slice is a fraction of the whole. If a category represents 25 out of a grand total of 200, its share is 25 / 200 = 0.125, so its angle is 0.125 × 360 = 45 degrees. Because the fractions of all categories add up to 1, the angles always add up to 360 degrees.

Worked example

Suppose a monthly budget of $2,000 splits into Rent $900, Food $500, Transport $300, and Savings $300. The angle for each slice is its amount divided by 2,000, times 360:

  • Rent: (900 / 2000) × 360 = 162° (45%)
  • Food: (500 / 2000) × 360 = 90° (25%)
  • Transport: (300 / 2000) × 360 = 54° (15%)
  • Savings: (300 / 2000) × 360 = 54° (15%)

The four angles sum to 162 + 90 + 54 + 54 = 360 degrees, which confirms the arithmetic.

Why you need it

When you draw a pie chart by hand or with a protractor, you have to know how many degrees each wedge occupies. Spreadsheet tools do this automatically, but the angle is still the underlying quantity, and knowing it lets you check a chart, mark a wedge precisely, or convert a percentage back into the geometry of the circle.

Handy reference points

A few percentages map to angles worth memorizing: 100% is 360°, 50% is 180° (a half circle), 25% is 90° (a right angle), 10% is 36°, and 1% is 3.6°. To go from a percentage straight to an angle, multiply the percentage by 3.6.

Frequently Asked Questions

How do you calculate the angle of a pie chart slice?
Divide the category's value by the total of all values, then multiply by 360 degrees: angle = (value / total) × 360. For example, a category of 25 out of a total of 200 gives (25 / 200) × 360 = 45 degrees.
Do all the slice angles add up to 360 degrees?
Yes. Because each slice is a proportion of the whole and the proportions sum to 1 (100%), the angles always sum to 360 degrees, the number of degrees in a full circle. If your slices do not sum to 360, a value or the total is wrong.
How do I convert a percentage into a pie chart angle?
Multiply the percentage by 3.6. Since 100% corresponds to 360 degrees, each 1% equals 360 / 100 = 3.6 degrees. For instance, 30% is 30 × 3.6 = 108 degrees.
What total should I use?
Use the sum of every category's value, so that the whole pie represents 100% of your data. If you only have one category's value and its percentage, you can also treat the total as 100 and the value as the percentage.

Related calculators